Free Slip Boundary Condition Calculator

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Overview

In fluid mechanics, the free slip condition implies that the velocity gradient normal to the boundary is zero, meaning the wall does not exert a viscous drag force on the fluid. This is frequently used as an approximation in high-Reynolds-number flow simulations where boundary layer effects are neglected or in idealized inviscid flow models. It contrasts with the no-slip condition, where fluid velocity at the boundary is assumed to be equal to the boundary's velocity.

Symbols

Variables

${\mu }_1$ = Dynamic Viscosity, $\frac{d{v}_x}{dy}$ = Velocity Gradient, $\tau$ = Shear Stress, ${\tau }_w$ = Shear Stress

Apply it well

When To Use

When to use: Apply when modeling idealized flows or regions far from solid surfaces where viscous wall effects are negligible.

Why it matters: It simplifies the Navier-Stokes equations for computational fluid dynamics by removing the need to resolve viscous boundary layers at specific interfaces.

Avoid these traps

Common Mistakes

• Assuming free-slip applies to real viscous fluids near walls in low-speed flows.
• Confusing free-slip with symmetry boundary conditions.

One free problem

Practice Problem

For a fluid with a dynamic viscosity of 0.001 Pa·s, what is the required velocity gradient (dvx/dy) at a wall if the free slip boundary condition is satisfied?

Solve for: $dv{x}_{d}y$

Hint: The formula equates the product of negative viscosity and the velocity gradient to zero.

The full worked solution stays in the interactive walkthrough.

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Related Formulas

References

Sources

1. White, F. M. (2011). Fluid Mechanics (7th ed.). McGraw-Hill Education.
2. Munson, B. R., Young, D. F., & Okiishi, T. H. (2006). Fundamentals of Fluid Mechanics. Wiley.
3. NIST CODATA
4. IUPAC Gold Book
5. Wikipedia: Free-slip boundary condition
6. White, Frank M. Fluid Mechanics. 8th ed., McGraw-Hill Education, 2016.
7. NIST Chemistry WebBook
8. White, Frank M. Fluid Mechanics. McGraw-Hill Education, 2016.